The high strength-to-weight ratio property of titanium aluminide (TiAl) based intermetallic alloys makes researchers regard this type of material as a potential replacement for the heavier superalloys of nickel. These alloys have been applied as turbocharger wheels of automobile and turbine blades of aircraft engines. A much recent alloy type of TiAl called the TNM alloy has emerged and primarily amenable to mechanical working; while providing the best combinations of mechanical properties that could be achieved through manufacturing processes with subsequent heat treatments. This is attained by solidifying entirely through the disordered β-phase (A2 structure). Effects of major alloying elements such as strength improvement, microstructural stability and phase formation demand the understanding of these alloying elements addition in TiAl-based intermetallic alloys. This review paper aims at encapsulating several works regarding the effects of major alloying elements on β-solidifying TiAl-based alloys and summarizing the characteristic effects of Si for these types of alloys. An impetus for future works on these types of intermetallic TiAl-based alloys is also presented.